nicematrix
allows you to set the column width.
\documentclass{article}
\usepackage{nicematrix}
\begin{document}
First, we write this system using matrices.
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{bNiceArray}
\]
We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{bNiceArray}
\]
Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final
\[
\begin{bNiceArray}[columns-width = 2em]{RRR|R}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{bNiceArray}
\]
\end{document}

You could also measure the widest entry and use its width.
\documentclass{article}
\usepackage{nicematrix}
\begin{document}
\setbox0\hbox{$-27$}%
\edef\mywd{\the\wd0}%
First, we write this system using matrices.
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
7 & 5 & 3 & 1\\
-2 & -3 & -4 & -5\\
\end{bNiceArray}
\]
We preform $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} - 7\mathbf{R_{1}}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} + 2\mathbf{R_{1}}$
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
0 & -9 & -18 & -27\\
0 & 1 & 2 & 3\\
\end{bNiceArray}
\]
Next we $\mathbf{R_{2}} \rightarrow \mathbf{R_{2}} \times -\frac{1}{9}$ and $\mathbf{R_{3}} \rightarrow \mathbf{R_{3}} - \mathbf{R_{2}}$, for final
\[
\begin{bNiceArray}[columns-width=\mywd]{RRR|R}
1 & 2 & 3 & 4\\
0 & 1 & 2 & 3\\
0 & 0 & 0 & 0\\
\end{bNiceArray}
\]
\end{document}

\phantom{-}
– Au101 Jun 2 '20 at 19:25array
package) try\begin{array}{*{3}{>{\centering}p{1cm}}|>{\centering}p{1cm}}
(adjust lengths to taste) – Au101 Jun 2 '20 at 19:29